Digital signal and image processing is generally computationally intensive. Quantum computing techniques offer the potential of exponential speedup of signal and image processing. While quantum Fourier and some quantum wavelet transforms are known, their direct application to signal and image processing is unclear. Classical solutions to signal and image processing generally cannot be directly simulated in a quantum environment. Rather, signal and image processing problems generally have to be reformulated in the quantum context, to take advantage of quantum computing techniques.
While image processing based upon solving partial differential equations (PDEs) is known, image enhancement is generally done using nonlinear PDEs. The computational cost to solve the nonlinear PDEs generally make such signal and image processing prohibitive. What is needed is a method for performing signal and image processing that exploits both classical and quantum parallelism. What is further needed is a method that provides useful signal and image processing without the heavy overall set of requirements for a full phase-coherent quantum computer.